Quadrature formulas associated with rational modifications of the Chebyshev weight functions
✍ Scribed by L. Darius; P. González-Vera; M. Jiménez Paiz
- Publisher
- Elsevier Science
- Year
- 2006
- Tongue
- English
- Weight
- 593 KB
- Volume
- 51
- Category
- Article
- ISSN
- 0898-1221
No coin nor oath required. For personal study only.
✦ Synopsis
Making use of the connection between quadrature formulas on the unit circle and the interval [-1, 1] recently established in [1], explicit expressions for the nodes and the weights of the Gaussian formulas associated with rational modifications of the Chebyshev weight functions, are given. Some illustrative numerical examples are also presented.
📜 SIMILAR VOLUMES
We consider interpolatory quadrature formulae, relative to the Legendre weight function on [-1, 1], having as nodes the zeros of the nth-degree Chebyshev polynomial of the third or fourth kind. Szeg5 has shown that the weights of these formulae are all positive. We derive explicit formulae for the w
A well known formula for evaluating Toeplitz determinants with rational generating functions due to DAY [Trans. Amer. Math. SOC. 206 (1975), 224 -2451 is complemented by a little known formula involving determinant of reduced order. The latter formula is used to evaluate some Toeplitz determinants w